Lottries: "Cash or annuity?" Why ask this when the ticket is purchased?

Factual Questions
41

That seems to be a long, long time for the lottery corporation to leave the choice open. Are the annuity payments and cash payments fixed at the beginning of that term, with the winner allowed to exercise his option to switch at any time through that period?

The strategy in that case would seem to be just to wait six months, and then call your friendly insurance salesman to find out how much of an annuity his firm would give you for the cash value - then decide whether you want his or the lottery corp’s. Long term interest rates can move substantially in six months and I am curious as to how the lottery corporation accounts for this…perhaps by only fixing the annuity terms when the decision is made final, or perhaps by hedging the exposure with options and charging the cost of the options to the prize fund?

Anybody know?

42

I calculated it this way:

For cash, ending balance after 20 years: (102)*(1.085^20) = 102 million initial investment, 8.25% return on the money, compounded yearly for 20 years.
Ending balance(cash) = 497.91 million

For annuity, ending balance after 20 years =

(((195/20)*1.0825 + 195/20)*1.0825) + 195/20)*1.0825…

= 496.57

Here is the perl script:

#!/usr/bin/perl -w

$intrate = .0825;
$endingbal = 102;
$contrib = 0;

for ($i = 0; $i < 20; $i++) {

$endingbal += $contrib;
$endingbal *= (1.0 + $intrate);

}

print "ending bal(cash) = $endingbal
";

$endingbal = 0;
$contrib = 195.0/20.0;
for ($i = 0; $i < 20; $i++) {

$endingbal += $contrib;
$endingbal *= (1.0 + $intrate);

}

print "ending bal(annuity) = $endingbal
";